Making Proficiency in Math : Making Proficiency in Math Soar to Greater Heights
November 2, 2006
Claudia Ahlstrom
Agenda : Agenda Look at the data
Review released NMSBA item
Look at NM Math Standards
Standards-based classroom
Implementing connections
Instructional materials
Cognitive demand
Resources
Math Grade 4 – ascending items : Math Grade 4 – ascending items Difficulty
Type of item
Score
Item number
Proficiency levels
Grade 4 Math OE : Grade 4 Math OE Points 0 1 2 3 4
Total % 16 16 27 30 10
Hi 1 4 20 48 28
Mid 9 17 34 32 7
Low 50 25 15 4 0
4th grade item : 4th grade item Do this problem and be thinking about:
What students need to know & be able to do to be successful on this type of task.
NM Math Standards : NM Math Standards Number & Operations
Algebra
Geometry
Measurement
Data Analysis & Probability
Process Standards : Process Standards Problem Solving
Reasoning & Proof
Communication
Connections
Representations
Classroom Experiences : Classroom Experiences What types of classroom experiences do students need to be prepared for NMSBA?
What should curriculum & instruction look like to support this type of learning?
What might a standards-based classroom look like?
What kind of support will teachers need to implement this type of curriculum?
Improving Mathematics Teaching : Improving Mathematics Teaching James Stigler & James Hiebert
Cultural Nature of Teaching
Making connections v. using procedures
Implementating connections problems
Instructional Materials : Instructional Materials What are the characteristics of the kinds of instructional materials that would best support content & process standards-based instruction?
MC² Rationale for Program Recommendations : MC² Rationale for Program Recommendations Math Content:
Problem Solving
Connections
Communication & Representation
Reasoning & Proof
Comprehensive & Standards Based
Instructional Design and Student Experiences:
Clear Goals & Deep Understanding
Active Learners
Explore Math using Manipulatives & Technology
Teacher Role:
Tasks and Lessons for Students
Sense Making & Facilitating Learning
Assessment:
Integrated into Instructional Program
Category 1 – Mathematics Content Processes : Category 1 – Mathematics Content Processes Reflects problem solving nature of mathematics & thinking that mathematicians use.
Makes connections within mathematics and between disciplines.
Incorporates mathematics as communication and representation into the program.
Incorporates mathematics as reasoning and proof into the program.
Is comprehensive & includes math content emphasized in NM Standards and Benchmarks at each grade level.
Category 2 – Instructional Design : Category 2 – Instructional Design 1. States learning goals clearly and explicitly and students are asked to work on
worthwhile mathematical tasks.
2. Is coherent and attends to students’ prior knowledge.
3. Provides extensive use of open-ended, free response, questions.
4. Incorporates calculators, computers and/or other technology into the program as
tools for students to use to do mathematics.
5. Is appropriate for all students.
6. Provides differentiated instructional strategies to address diverse learning needs
(i.e., ELL and SPED).
7. Supports learning at home.
Category 3 – Student Experiences : Category 3 – Student Experiences 1. Designed so students are active learners.
2. Designed for students to construct their own understanding of mathematics.
3. Asks students to engage in mathematical discourse.
4. Provides manipulatives and/or technology to explore mathematical ideas, model mathematical situations, analyze data, calculate numerical results and solve problems.
5. Expects students to determine when they need to calculate in a problem and whether they require an exact or approximate answer.
6. Expects students to reflect on, make judgments about, and report on their own thought process, problem solving attempts, and performance.
7. Provides user-friendly students’ materials
Category 4 – Teacher Role: Instructional Materials : Category 4 – Teacher Role: Instructional Materials 1. Provide suggestions to teachers so that in tasks and lessons teachers can help students.
2. Provide suggestions for teachers in initiating and orchestrating mathematical discourse.
3. Provide assistance to teachers to facilitate learning by all students.
4. Provide suggestions to teachers for establishing a student centered classroom learning environment.
5. Provide suggestions to teachers to help them reflect on what happened in the classroom so that they can adjust or adapt their teaching plans.
Category 5 – Assessment : Category 5 – Assessment 1. Integrates content and process standards into the instructional program
2. Uses multiple means of assessment, informal as well as formal
3. Includes assessment tasks making connections between mathematical ideas.
4. Assesses conceptual understanding and procedural knowledge frequently through tasks that ask students to apply information about a given concept in novel situations.
Cognitive Demand : Cognitive Demand Memorization Tasks
Procedures without Connections Tasks
Procedures with Connections Tasks
Doing Mathematics Tasks
Resources : Resources Tasks: NAEP, BAM
Instructional Materials: MC², NCREL, TERC,